Turnabout Puzzle
by renrenren3
Summary: Layton and Phoenix hang out at a café. Predictably, Layton is reminded of a puzzle.


Written for artrica for the layton_exchange. I jumped at the chance of writing a crossover between those two. Since I know nothing about the crossover game (apart that it'll be epic) I made up things about those four's friendship. The puzzle about the three teacups isn't made up, I got it from _'The Canterbury Puzzles'_ by Dudeney. Despite Nick's objections, Layton is right: every puzzle has an answer.

-x-

With miles and miles of ocean between the States and England, it wasn't as if Phoenix and Maya got to hang out with Luke and the Professor very often. Most of the time Maya and Luke thought this was a pity, since the two of them had become very good friends. Even Phoenix and Layton, after their initial disagreement, had found out that they had a lot in common.

It was when they all met up that they all remembered why it was a good thing that they lived so far apart. This time they were in San Francisco: Layton was here for a seminar and Maya had jumped at the chance to spend a couple of days with her English friends.

They'd barely had the time to say hello when the Professor suddenly mentioned a puzzle. Now they were all sitting at a small round table outside a café and had already gone through several coffees, a slice of pie each and two hamburgers for Maya. The discussion was still in full swing.

"Let me state the problem again," Layton said for what was probably the hundredth time. "You have three cups and ten cubes of sugar..."

"Hold it!" Phoenix exclaimed, banging his hand on the table and making Luke jump. "What kind of cups?"

Layton raised his eyebrows, clearly appalled by this ungentlemanly behaviour, but rallied magnificently. "Common teacups. Made of white porcelain. I beg your pardon but that's not relevant."

"I'll decide what's relevant or not," Phoenix replied, a bit stiffly, but he nodded for Layton to continue. As the other man repeated his puzzle once more, Phoenix leaned towards Maya and whispered, "A little help here?"

"Come on, Nick!" she whispered, her words slightly muffled by a mouthful of food. "You're not in the courtroom, it's just a silly little quiz."

Phoenix passed one hand nervously through his hair. "But I have no idea about the solution," he whined. "Have _you_ solved it?"

Maya snorted, recognizing the other man's _'I hate losing'_ voice. "I have no idea," she said. "Luke?"

"Hmm?"

Layton's miniature assistant was scratching his head and looked deep in thought.

"Any luck with the puzzle?" Maya asked him.

"Not yet," Luke replied. "But I'm working on it."

"I'm sure you'll be able to solve this puzzle, Luke," the Professor said.

Phoenix shook his head. "That's impossible!" he said. "There's no way to arrange ten cubes into three cups so that every cup contains an odd number of cubes," he insisted. He'd already tried to point that out earlier, but to no avail.

Now he looked at Maya for support, but she simply shrugged. "I don't think the Professor would give us a puzzle without an answer," she said.

Layton smiled to himself and took another sip of tea.

"Oh, I don't know, sometimes he does," Luke ventured. "To make me think outside the box, you know..."

"That's it, then!" Phoenix exclaimed, pointing an accusatory finger at Layton. "You've been tricking us for all this time with an impossible puzzle."

Layton kept smiling. "I assure you that there is a perfectly plausible solution," he said, ignoring the way Phoenix's finger was poking him in the chest. "But if you're really sure that it's impossible, you should prove it. A gentleman never makes any unsubstantiated claims."

Proving things, now that was more of Phoenix's area of expertise. He could definitely find some evidence here. He grabbed his own teacup from the table (unused, since he was more of a coffee person) and waved it under Layton's nose.

"Take that!" he said triumphantly. "This proves beyond any doubt that your puzzle is impossible. Case closed."

Maya looked at the teacup and then back at Phoenix. "Nick, are you sure about this?" she asked in a small voice.

"Of course," Phoenix lied, slightly annoyed at the fact that she had been the first one to object. She was supposed to be on _his_ side!

Layton simply chuckled. "I'm sorry but I think that's incorrect," he said. "Maybe you would care to try again?"

"Uhm," said Luke.

Maya shook her head. "I get the feeling that the Judge should be around to scold you," she told Phoenix.

Phoenix gave an apologetic grin and quickly looked around to see if there was anything else on the table that he could use as evidence. The best thing would be to have actual sugar cubes but they only had some packets of artificial sweetener. Maybe he could ask the waitress for some sugar cubes.

Showing Layton the leftover pie or his attorney badge would probably yield no results, but he could always try if he ran out of options.

Phoenix frowned. He had the nagging suspicion that his usual technique of presenting random pieces of evidence until a suspect let something slip wasn't going to work on Layton. The Professor's poker face was just too good. And, speaking of poker, at some later point Phoenix was going to ask him if he played cards, but right now he had a case to solve. Puzzle. Whatever.

"Are you all right?" Maya asked.

Phoenix sighed. "I don't like admitting it but I'm really stumped on this one," he said. "It's your win, Professor. Now can you tell us the solution?"

"Oh," Layton said, and his face fell a little. "I'm not used to having people give up on solving puzzles."

From his tone it sounded as if England was full of puzzle-lovers who did nothing else but think of puzzles all day long. Phoenix refrained from commenting and simply shrugged. "Sorry about that but I've got nothing."

He looked at Maya, who shook her head. "Me neither," she replied cheerfully. "But I'm curious to see the solution."

"Uhm," Luke said, and then he held up his sketchbook. "I think I've solved it." Phoenix's jaw dropped as he saw a crayon drawing of the correct answer.

"Luke, my boy, that's the correct answer," Layton said, brightening up considerably. "Good job!"

Maya winked at Phoenix. "I think that was a win for Team England," she said. "You've got to do better than this if you want to keep ahead of the game."

"You're supposed to be on _my_ team!" Phoenix hissed. "And since when do we have teams anyway?"

The Professor smiled in his tea. "Speaking of teams, this reminds me of a puzzle..."


End file.
